<div dir="ltr">And we do not have sparse LU on GPUs so that is done on the CPU.<div><br></div><div>And I don't know why it would not weak scale well. </div><div>Your results are consistent with just using one process with one domain, (re Matt) while you double the problem size.</div></div><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">On Tue, Nov 4, 2025 at 2:27 PM Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">On Tue, Nov 4, 2025 at 1:25 PM Angus, Justin Ray via petsc-dev <<a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a>> wrote:</div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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Hi Junchao,</div>
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We have recently been using ASM + LU for 2D problems on both CPU and GPU. However, I found that this method has very bad weak scaling. I find that the cost of PCApply increases by about a factor of 4 each time I increase the problem size in 1 dimension by a
factor of 2 while keeping the load per core/gpu the same. The total number of GMRES iterations does not increase, just the cost of PCApply (and PCSetup). Is this scaling behavior expected? Any ideas of how to optimize the preconditioner?</div></div></blockquote><div><br></div><div>The cost of PCApply for ASM is dominated by the cost of process-local block solves. You are using LU for the block solve. (Sparse) LU has cost roughly O(N^2) for the apply (depending on the structure of the matrix). So, if you double the size of a local block, your runtime should increase by about 4x. Thus LU is not a scalable method.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div>
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Thank you.</div>
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-Justin</div>
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<b>From: </b>Junchao Zhang <<a href="mailto:junchao.zhang@gmail.com" target="_blank">junchao.zhang@gmail.com</a>><br>
<b>Date: </b>Monday, April 14, 2025 at 7:35 PM<br>
<b>To: </b>Angus, Justin Ray <<a href="mailto:angus1@llnl.gov" target="_blank">angus1@llnl.gov</a>><br>
<b>Cc: </b><a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a> <<a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a>>, Ghosh, Debojyoti <<a href="mailto:ghosh5@llnl.gov" target="_blank">ghosh5@llnl.gov</a>><br>
<b>Subject: </b>Re: [petsc-dev] Additive Schwarz Method + ILU on GPU platforms<br>
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<div dir="ltr">Petsc supports ILU0/ICC0 numeric factorization (without reordering) and then triangular solve on GPUs. It is done by calling vendor libraries (ex. cusparse).</div>
<div dir="ltr">We have options -pc_factor_mat_factor_on_host <bool> -pc_factor_mat_solve_on_host <bool> to force doing the factorization and MatSolve on the host for device matrix types.</div>
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<div dir="ltr">You can try to see if it works for your case.</div>
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<div dir="ltr" class="gmail_signature">--Junchao Zhang</div>
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<div dir="ltr" class="gmail_attr">On Mon, Apr 14, 2025 at 4:39 PM Angus, Justin Ray via petsc-dev <<a href="mailto:petsc-dev@mcs.anl.gov" target="_blank">petsc-dev@mcs.anl.gov</a>> wrote:</div>
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<p class="MsoNormal"><span style="font-size:11pt">Hello,</span></p>
<p class="MsoNormal"><span style="font-size:11pt"> </span></p>
<p class="MsoNormal"><span style="font-size:11pt">A project I work on uses GMRES via PETSc. In particular, we have had good successes using the Additive Schwarz Method + ILU preconditioner setup using a CPU-based code. I found online where it is stated that
“Parts of most preconditioners run directly on the GPU” (<a href="https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!bw6qeKcY7MKSvlEgcogdKR7fpjZSOFvka6zfDprUZ_sJHdE-YZmRD6UTqWQW3_uGVBII4P-AG0zaGTLbI67_fQ$" style="margin-top:0px;margin-bottom:0px" target="_blank">https://petsc.org/release/faq/</a>).
Is ASM + ILU also available for GPU platforms?</span></p>
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<p class="MsoNormal"><span style="font-size:11pt">-Justin</span></p>
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</blockquote></div><div><br clear="all"></div><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!dXQeQOf4ckc4MRP64tltlc6e1FJgPXuEuzX8tHsTreO_vIP2Lbge1es994i-WdQTd1zpmNP2R9dbEHfLa0v_$" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>
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